Question

When the pressure of an ideal gas is doubled in an isothermal process. the root mean square speed of molecules
a)increases by the factor sq.root2
b)decreases by the factor sq.root2
c)does not change

Answer 1

Answer:

Root mean square velocity v rms = sqrt (3 PV/ M) or sqrt (3RT / M)

When pressure is doubled at constant temperature, then volume becomes half ( PV = RT) and PV remains constant ( Boyle's law). That's why v rms speed remains unchanged.

♥️Option ( C ) is correct.

Answer 2

Explanation:

The rms speed of gas molecules is given by :

$v_{rms}=\sqrt{\dfrac{3RT}{M}}$ ......(1)

R is gas constant

T is temperature

M is mass

Since, $PV=RT$

So, formula becomes :

$v_{rms}=\sqrt{\dfrac{3PV}{M}}$

When the pressure of an ideal gas is doubled in an isothermal process, new rms speed becomes :

If P' = 2P

As pressure is doubled, volume becomes half. such that,

$v'_{rms}=\sqrt{\dfrac{3P'V}{M}}\\\\v'_{rms}=\sqrt{\dfrac{3(2P)(V/2)}{M}}\\\\v'_{rms}=\sqrt{\dfrac{3P'V}{M}}\\\\v'_{rms}= v_{rms}$

So, new rms speed of the ideal gas remains the same.

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Ideal gas

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